Adaptive event‐triggered safety control for multiplayer mixed zero‐sum game with partial inputs delay

Abstract This paper proposes an adaptive safety control method applicable to a multiplayer mixed zero‐sum (MZS) game of nonlinear systems with partial inputs delay. Firstly, a framework is introduced involving N players, where player 1 and player N form a zero‐sum (ZS) game, and player 1 and players 2 to N‐1 form nonzero‐sum (NZS) games, with some players experiencing time delays. Subsequently, the system's value function is augmented with a control barrier function (CBF) to ensure that the system's state remains within a safe region. Secondly, to approximate Nash equilibrium solutions, the study employs adaptive dynamic programming (ADP) and utilizes a critic‐only neural network (NN) to approximate optimal solutions. Diverging from traditional time‐trigger methods, computational and communication load reduction is achieved by introducing a state‐related event trigger condition. The stability of the system is then meticulously analyzed using the Lyapunov theorem. Finally, to validate the effectiveness of the proposed method, the study provides a simulation example demonstrating its performance. In summary, this research introduces an efficient adaptive safety control method for addressing multiplayer MZS games with partial inputs delay, incorporating CBFs, ADP, and state‐related event triggering.